Modelling and characterization of thin film planar capacitors: inherent errors and limits of applicability of partial capacitance methods

Abstract

The analytical partial capacitance methods (PCM) widely accepted for calculation of properties of capacitors with planar electrodes, coplanar strip waveguides (CPS) and coplanar waveguides (CPW) are reviewed based on the challenges met during the development and tailoring of (Ba, Sr)TiO3 thin films fabricated on different types of substrates. An alternative view on the conformal mapping method is given, a correction for electrodes of finite thickness is introduced and the applicability of easy-to-use simplified analytical equations is reviewed and extended. Calculation results obtained with different models are compared against the results of FEM numerical simulation in the parameter range relevant for development of tuneable ferroelectric films. The models were found to be less accurate than previously reported. Accordingly, guidelines for extending the applicability domain and for minimizing the inherent errors of the analytical models are presented. The discussion is focused on the possible improvements of the measurement techniques.

Techniques for measuring the microwave dielectric properties of materials

“…Techniques for the dielectric characterization of sheet-like materials and films at microwave frequencies are currently being developed [18,272,279,284]. In contrast to the major impact of thin materials in many applications, such as tunable microwave devices, so far their electrical properties were mostly determined at low frequencies [285][286][287][288] or by optical methods [289,290].…”

“…Future developments may promote Hilbert-transformation spectroscopy with the potential to cover the broad range from some gigahertz to some terahertz [291,292]. Presently the method is considered a tool for liquid identification in security applications [287].…”

Combined effects of thickness, grain size and residual stress on the dielectric properties of Ba0.5Sr0.5TiO3 thin films

“…The capacitance C and the dielectric losses tanδ of the films were measured using an impedance analyzer (HP 4284 A, Keysight, Santa Rosa, USA) at 100 kHz and room temperature. The capacitance-voltage characteristics were determined with the following DCbiasing scheme: 0V → + 40 V → 0 V → -40 V → 0 V. The dielectric permittivity ε' of the films was calculated using the modified partial capacitance method (PCM) [39,40]. …”

Analytically describing the temperature-dependent constitutive parameters of an electromagnetic metamaterial

“…However, the FR4 is relatively thin, with a lower dielectric constant; neglecting this term overestimates the change in capacitance and the resonant frequency (Chiam et al, 2010). An alternative expression for the capacitance of coplanar strips, which captures the fields on the posterior side of the metamaterial, is given by Vukadinovic et al (2009):…”